Hannover initially threatened Bayern on the break, but the champions quickly became alert to the hosts' game plan and stifled them to great effect before unsurprisingly taking a 25th-minute lead.
Thomas Muller surged into the area with a late run from deep to head in a precise Rafinha cross and Hannover rarely looked like getting back into the contest.
Thiago Alcantara doubled Bayern's lead nine minutes later, but he owed much to the assist.
Bastian Schweinsteiger chipped a pin-point pass into the area for Thiago and the midfielder powerful struck past Ron-Robert Zieler after bringing the ball down confidently.
Bayern had to wait until the 59th minute before their next goal as Muller slotted in his second following a clever flick from Mario Mandzukic.
The runaway leaders added a fourth for good measure seven minutes later as Mandzukic deservedly found the net with a header from another Rafinha cross, meaning Bayern end the weekend 19 points clear of second-placed Bayer Leverkusen. Hannover stay 11th.
The day's other match saw Eintracht Frankfurt held by 10-man Werder Bremen at the Commerzbank-Arena, despite dominating from start to finish.
Former Real Madrid attacker Joselu missed a great chance early on for the hosts, but he could only poke wide when one-on-one with Raphael Wolf.
Alexander Meier hit the outside of the right post from a free-kick and the hosts were given even more of an advantage in the 33rd minute as Felix Kroos received a second yellow card.
Frankfurt were consigned to a draw in the final three minutes as Meier headed wide from close range, meaning they stay in 13th with 22 points, above Bremen on goal difference.
